• Open Access

BPS property and its breaking in 1+1 dimensions

C. Adam and A. Wereszczynski
Phys. Rev. D 98, 116001 – Published 10 December 2018

Abstract

We show that the Bogomol’nyi-Prasad-Sommerfield (BPS) property is a generic feature of all models in (1+1) dimensions that does not put any restriction on the action. Here, by BPS solutions we understand static solutions that (i) obey a lower-order Bogomolny-type equation in addition to the Euler-Lagrange equation, (ii) have an energy that only depends on a topological charge and the global properties of the fields, but not on the local behavior (coordinate dependence) of the solution, and (iii) have zero pressure density. Concretely, to accomplish this program we study the existence of BPS solutions in field theories where the action functional (or energy functional) depends on higher than first derivatives of the fields. We find that the existence of BPS solutions is a rather generic property of these higher-derivative scalar field theories. Hence, the BPS property in 1+1 dimensions can be extended not only to an arbitrary number of scalar fields and k-deformed models, but also to any (well-behaved) higher-derivative theory. We also investigate the possibility to destroy the BPS property by adding an impurity that breaks the translational symmetry. Further, we find that there is a particular impurity-field coupling that still preserves one-half of the BPS-ness. An example of such a BPS kink-impurity bound state is provided.

  • Received 25 October 2018

DOI:https://doi.org/10.1103/PhysRevD.98.116001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

C. Adam1 and A. Wereszczynski2

  • 1Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela, Spain
  • 2Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków 31-007, Poland

Article Text

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Issue

Vol. 98, Iss. 11 — 1 December 2018

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